Yang Hu

Enumerating vector bundles of a fixed rank over a given manifold is a classical question in topology. While vector bundles are stably computable via K-theory, in the unstable range they become much harder to detect. In this talk, we will demonstrate...

A ring spectrum (a.k.a. a multiplicative cohomology theory) E is complex-orientable if every complex vector bundle admits a Thom class in E . While many familiar spectra are complex-orientable, notable examples fail to be so — such as real K-theory...

Pick your favorite manifold M and a positive integer r : how many r rank (topological) complex vector bundles are there over M up to isomorphism? While the question is accessible via K-theory in the stable range, unstably such bundles become much...